Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

(1)  2, 4, 8

(2)  4, 8, 16

(3)  1, 2, 1

(4)  0.5, 1, 2

A blind person after walking 10 steps in one direction, each of length 80 cm, turns randomly to the left or to the right by $90°.$ After walking a total of 40 steps the maximum possible displacement of the person from his starting position could be -

(1)  $320 \mathrm{m}$

(2)  $32 \mathrm{m}$

(3)  $16/\sqrt{2} \mathrm{m}$

(4)  $16\sqrt{2} \mathrm{m}$

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is -

1. $120°$

2.  $150°$

3.  $135°$

4.  None of these

The three vectors OA, OB and OC have the same magnitude R. Then the sum of these vectors have magnitude -

1. $\mathrm{R}$

2. $\sqrt{2}\mathrm{R}$

3. $3\mathrm{R}$

4. $\left(1+\sqrt{2}\right)\mathrm{R}$

A truck travelling due north with 20m/s turns towards west and travels at the same speed. Then the change in velocity is -

(1)  40 m/s north-west

(2)  $20\sqrt{2}$ m/s north-west

(3)  40 m/s south-west

(4)  $20\sqrt{2}$ m/s south-west

A particle is moving in a circle of radius r centered at O with constant speed v. The change in velocity moving from A to B $\left(\angle \mathrm{AOB}=40°\right)$ is -

(A)  $2\mathrm{v} \cos 40°$

(B)  $2\mathrm{v} \sin 40°$

(C)  $2\mathrm{v} \cos 20°$

(D)  $2\mathrm{v} \sin 20°$

What is the resultant of three coplanar forces: $300 \mathrm{N}$ at $0°$, $400 \mathrm{N}$ at $30°$ and $400 \mathrm{N}$ at $150°$?

1.  $500 \mathrm{N}$

2.  $700 \mathrm{N}$

3.  $1100 \mathrm{N}$

4.  $300 \mathrm{N}$

Two forces, ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ are acting on a body. One force is doubled of the other force and the resultant is equal to the greater force. Then the angle between the two forces is -

(A)  ${\cos }^{-1} \left(1/2\right)$

(B)  ${\cos }^{-1} \left(-1/2\right)$

(C)  ${\cos }^{-1} \left(-1/4\right)$

(D)  ${\cos }^{-1} \left(1/4\right)$

If the angle between vector a and b is an acute angle, then the difference a$-$b is -

(1)  the main diagonal of the parallelogram

(2)  the minor diagonal of the parallelogram

(3)  any of the above

(4)  none of the above